Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #509 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#2161 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | C2×D8 |
| commutator | C8 | C22×C4×C17 |
| Frattini, cosocle | C2×C8 | C23×C17 |
| socle | C2×C17 | C2×#107 |
| prime radical | C23×C17 | Q16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ C22×C8×C17 ◁ G | |
140 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,27,24,28,23,38)(20,29,33,45,31,43,34,48)(21,35,36,42,37,49,30,26)(25,39,41,47,40,46,44,32);(18,20,30,46,23,34,37,47,24,31,36,39,22,33,21,32)(19,25,35,45,27,41,42,43,28,40,49,48,38,44,26,29);(20,31)(25,40)(29,43)(32,47)(33,34)(39,46)(41,44)(45,48)544 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 893);